Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                <p type="main">
                  <s>
                    <pb xlink:href="039/01/461.jpg" pagenum="433"/>
                  partes innumeras æquales, & a partibus ſingulis
                    <emph type="italics"/>
                  F
                    <emph.end type="italics"/>
                  ad diame­
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                    <arrow.to.target n="note462"/>
                  trum
                    <emph type="italics"/>
                  BD
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                  demittantur ſinus
                    <emph type="italics"/>
                  FY.
                    <emph.end type="italics"/>
                  Et ſumma quadratorum ex
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                  ſinibus omnibus
                    <emph type="italics"/>
                  FY
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                  æqualis erit ſummæ quadratorum ex ſinibus
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                  omnibus
                    <emph type="italics"/>
                  CY,
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                  & ſumma utraque æqualis erit ſummæ quadrato­
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                  rum ex totidem ſemidiametris
                    <emph type="italics"/>
                  CF
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                  ; adeoque ſumma quadrato­
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                  rum ex omnibus
                    <emph type="italics"/>
                  FY,
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                  erit duplo minor quam ſumma quadrato­
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                  rum ex totidem ſemidiametris
                    <emph type="italics"/>
                  CF.
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                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note462"/>
                  LIBER
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                  TERTIUS.</s>
                </p>
                <figure id="id.039.01.461.1.jpg" xlink:href="039/01/461/1.jpg" number="223"/>
                <p type="main">
                  <s>Jam dividatur perimeter circuli
                    <emph type="italics"/>
                  AE
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                  in particulas totidem æ­
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                  quales, & ab earum unaquaque
                    <emph type="italics"/>
                  F
                    <emph.end type="italics"/>
                  ad planum
                    <emph type="italics"/>
                  QR
                    <emph.end type="italics"/>
                  demittatur
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                  perpendiculum
                    <emph type="italics"/>
                  FG,
                    <emph.end type="italics"/>
                  ut & a puncto
                    <emph type="italics"/>
                  A
                    <emph.end type="italics"/>
                  perpendiculum
                    <emph type="italics"/>
                  AH.
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                  Et
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                  vis qua particula
                    <emph type="italics"/>
                  F
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                  recedit a plano
                    <emph type="italics"/>
                  QR,
                    <emph.end type="italics"/>
                  erit ut perpendiculum
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                  illud
                    <emph type="italics"/>
                  FG
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                  per hypotheſin, & hæc vis ducta in diſtantiam
                    <emph type="italics"/>
                  CG,
                    <emph.end type="italics"/>
                    <lb/>
                  erit efficacia particulæ
                    <emph type="italics"/>
                  F
                    <emph.end type="italics"/>
                  ad Terram circum centrum ejus con­
                    <lb/>
                  vertendam. </s>
                  <s>Adeoque efficacia particulæ in loco
                    <emph type="italics"/>
                  F,
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                  erit ad effi­
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                  caciam particulæ in loco
                    <emph type="italics"/>
                  A,
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                  ut
                    <emph type="italics"/>
                  FGXGC
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  AHXHC,
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                  hoc
                    <lb/>
                  eſt, ut
                    <emph type="italics"/>
                  FCq
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  ACq
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                  ; & propterea efficacia tota particularum
                    <lb/>
                  omnium in locis ſuis
                    <emph type="italics"/>
                  F,
                    <emph.end type="italics"/>
                  erit ad efficaciam particularum totidem in
                    <lb/>
                  loco
                    <emph type="italics"/>
                  A,
                    <emph.end type="italics"/>
                  ut ſumma omnium
                    <emph type="italics"/>
                  FCq
                    <emph.end type="italics"/>
                  ad ſummam totidem
                    <emph type="italics"/>
                  ACq,
                    <emph.end type="italics"/>
                  hoc
                    <lb/>
                  eſt, (per jam demonſtrata) ut unum ad duo.
                    <emph type="italics"/>
                  Q.E.D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>Et quoniam particulæ agunt recedendo perpendiculariter a
                    <lb/>
                  plano
                    <emph type="italics"/>
                  QR,
                    <emph.end type="italics"/>
                  idque æqualiter ab utraque parte hujus plani: eædem
                    <lb/>
                  convertent circumferentiam circuli Æquatoris, eiQ.E.I.hærentem
                    <lb/>
                  Terram, circum axem tam in plano illo
                    <emph type="italics"/>
                  QR
                    <emph.end type="italics"/>
                  quam in plano Æqua­
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                  toris jacentem. </s>
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